Hostname: page-component-7b7567c8c-wxvwp Total loading time: 0 Render date: 2026-11-14T12:57:06.803Z Has data issue: false hasContentIssue false
  • English
  • Français

Integrated processes and the discrete cosine transform

Part of:Inference from stochastic processesMathematical economics

Published online by Cambridge University Press:  14 July 2016

Robert B. Davies
Robert B. Davies*
Affiliation:
Statistics Research Associates Ltd
*
1 Postal address: Statistics Research Associates Limited, PO Box 12–649, Thorndon, Wellington, New Zealand. Email: robert@statsresearch.co.nz
Get accessRights & Permissions [Opens in a new window]

Abstract

A time-series consisting of white noise plus Brownian motion sampled at equal intervals of time is exactly orthogonalized by a discrete cosine transform (DCT-II). This paper explores the properties of a version of spectral analysis based on the discrete cosine transform and its use in distinguishing between a stationary time-series and an integrated (unit root) time-series.

Keywords

Beta-optimal testBrownian motionDCT-IIdiscrete cosine transformintegrated processrandom walkspectrumtime-seriesunit root

MSC classification

Primary:62M10: Time series, auto-correlation, regression, etc.
Secondary:62M15: Spectral analysis91B84: Economic time series analysis

Information

Type
Time series analysis
Information
Journal of Applied Probability , Volume 38 , Issue A: Probability, Statistics and Seismology , 2001, pp. 105 - 121
Copyright
Copyright © Applied Probability Trust 2001 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Davies, R. B. (1969). Beta-optimal tests and an application to the summary evaluation of experiments. J. Roy. Statist. Soc. Ser. B 31, 524–538.Google Scholar
Davies, R. B. (1973). Asymptotic inference in stationary Gaussian time-series. Adv. Appl. Probab. 5, 469–497.Google Scholar
Davies, R. B. (1980). The distribution of a linear combination of chi-squared random variables. Algorithm AS155. Appl. Statist. 29, 323–333.Google Scholar
Davies, R. B. (1983). Optimal inference in the frequency domain. In Time Series in the Frequency Domain (Handbook Statist. 3), eds Brillinger, D. R. and Krishnaiah, P. R., Elsevier, Amsterdam, 73–92.Google Scholar
Davies, R. B. (1985). Asymptotic inference when the amount of information is random. In Proc. Berkeley Conf. in Honor of Jerzy Neyman and Jack Kiefer , Vol. 2, eds LeCam, L. M. and Olshen, R. A., Wadsworth, Belmont, CA, 841–864.Google Scholar
Davies, R. B. (2000). Linear combination of chi-squared random variables. Available at http://www.statsresearch.co.nz/robert/QF.htm.Google Scholar
Dickey, D. A., Bell, W. R. and Miller, R. B. (1986). Unit roots in time series models: Tests and implications. Amer. Statistician 40, 12–26.Google Scholar
Harvey, A. C. (1989). Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press.Google Scholar
King, M. L. (1988). Towards a theory of point optimal testing. Econometric Reviews 6, 169–218.CrossRefGoogle Scholar
Rao, K. R. and Yip, P. (1990). Discrete Cosine Transform: Algorithms, Advantages, Applications. Academic Press, New York.CrossRefGoogle Scholar
Van Loan, C. (1992). Computational Frameworks for the Fast Fourier Transform. SIAM, Philadelphia.Google Scholar